RESEARCH ARTICLE PHYSICS
Giant facet-dependent spin-orbit torque and spin Hall conductivity in the triangular antiferromagnet IrMn3
2016 © The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC). 10.1126/sciadv.1600759
Weifeng Zhang,1,2* Wei Han,1,3* See-Hun Yang,1 Yan Sun,4 Yang Zhang,4 Binghai Yan,4 Stuart S. P. Parkin1,5† There has been considerable interest in spin-orbit torques for the purpose of manipulating the magnetization of ferromagnetic elements for spintronic technologies. Spin-orbit torques are derived from spin currents created from charge currents in materials with significant spin-orbit coupling that propagate into an adjacent ferromagnetic material. A key challenge is to identify materials that exhibit large spin Hall angles, that is, efficient charge-to-spin current conversion. Using spin torque ferromagnetic resonance, we report the observation of a giant spin Hall angle qeff SH of up to ~0.35 in (001)-oriented single-crystalline antiferromagnetic IrMn3 thin films, coupled to ferromagnetic permalloy layers, and a qeff SH that is about three times smaller in (111)-oriented films. For (001)-oriented samples, we show that the magnitude of qeff SH can be significantly changed by manipulating the populations of various antiferromagnetic domains through perpendicular field annealing. We identify two distinct mechanisms that contribute to qeff SH: the first mechanism, which is facet-independent, arises from conventional bulk spin-dependent scattering within the IrMn3 layer, and the second intrinsic mechanism is derived from the unconventional antiferromagnetic structure of IrMn3. Using ab initio calculations, we show that the triangular magnetic structure of IrMn3 gives rise to a substantial intrinsic spin Hall conductivity that is much larger for the (001) than for the (111) orientation, consistent with our experimental findings.
INTRODUCTION Spin-orbitronics is an emerging field of current interest in which spin-orbit coupling gives rise to several novel physical phenomena, many of which also have potential technological significance (1, 2). Of particular interest is the spin Hall effect in which conventional charge current densities (JC) are converted to pure spin current densities (ℏ2 JS) via spin-orbit coupling within the material (3, 4). The conversion efficiency is described by the spin Hall angle (SHA) qSH = eJS/JC. One of the most widely used techniques to measure SHA is by comparing the antidamping spin torque generated by a radio frequency (RF) spin current that propagates into an adjacent ferromagnetic layer with the field torque generated by an RF charge current (2, 5–9). This technique of spin torque ferromagnetic resonance (ST-FMR) yields an effective SHA, qeff SH (because, as we discuss further below, there can be other potential sources of spin current). The largest values of qeff SH in conventional metals that have been reported to date include the heavy metals b-tantalum (2), b-tungsten (7), platinum [once the interface transparency is taken into account (9)], and bismuth-doped copper (10). A prerequisite for large qSH is significant spin-orbit coupling. Of potential interest are compounds such as Ir1−xMnx, which are antiferromagnetic for various ranges of x. These compounds are widely used in spintronic devices because of the exchange bias fields that they imprint on neighboring ferromagnetic layers that lead to a unidirectional magnetic anisotropy (11). Theoretical studies predict that chemically ordered IrMn3 should exhibit a large anomalous Hall effect (AHE) due to its unusual triangular magnetic structure (12, 13), and recent experimental studies observed large AHE in the noncollinear 1
2
IBM Research–Almaden, San Jose, CA 95120, USA. Department of Materials Science Engineering, Stanford University, Stanford, CA 94305, USA. 3International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China. 4 Max Planck Institute for Chemical Physics of Solids, Dresden D-01187, Germany. 5 Max Planck Institute for Microstructure Physics, Halle (Saale) D-06120, Germany. *These authors contributed equally to the work. †Corresponding author. Email: [email protected]
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antiferromagnets (AFs) Mn3Sn and Mn3Ge (14–16). Here, we observed a giant qeff SH in Ir1−xMnx films and a large facet dependence of qeff SH on IrMn3, which we find can be markedly enhanced by manipulating the populations of various AF domains via annealing in magnetic fields oriented perpendicular, but not parallel, to the film layers.
RESULTS Microstrip devices, 10 mm wide and 100 mm long, are fabricated using standard optical lithography and ion milling techniques from Ir1−xMnx/permalloy (Py)/TaN films. The films are deposited by magnetron sputtering (see Materials and Methods for details) on Si(001) substrates (covered with 25-nm-thick SiO2), MgO (001) substrates, and Al2O3 (0001) substrates at room temperature (RT) in a high–vacuum deposition chamber. ST-FMR measurements are carried out by passing a high-frequency RF current into the device (JC is the charge current density in Fig. 1A) in the presence of an external field Hext that is applied in the plane at 45° to the microstrip. The charge current that flows in the Ir1−xMnx layer generates two distinct torques on the Py layer, namely, a spin-orbit torque and an Oersted field torque. The ^ is given by (5, 17) time derivative of the magnetization of Py m → → ^ ^ dm dm ^ H ef f þ am ^ H rf þ ^ ¼ gm gm dt dt
g
ℏ ^ s ^m ^Þ JS ðm 2m0 MS t
ð1Þ
→
where g is the gyromagnetic ratio; H eff is composed of the external field, the exchange bias field, and the out-of-plane demagnetization → field; a is the Gilbert damping constant; H rf is the Oersted field; ℏ 2 JS is the spin current density generated in the Ir1−xMnx layer; m0 is 1 of 8
RESEARCH ARTICLE as a function of Hext, measured on ~60 Å polycrystalline IrMn3 (p-IrMn3)/60 Å Py for RF frequencies varying between 9 and 14 GHz. As the RF frequency increases, the resonance field Hres increases, as expected from the Kittel model, and the magnitude of Vmix decreases. Vmix(Hext) has two components: an antisymmetric component due to the Oersted field–generated torque and a symmetric component that arises from the spin-orbit torque. The ST-FMR curves are fitted with symmetric and antisymmetric Lorentzian functions, according to (5, 9) "
Vmix
DH 2 DHðHext Hres Þ ¼ c VS 2 þ VA 2 DH 2 þ ðHext Hres Þ2 DH þ ðHext Hres Þ
#
ð2Þ where c is a constant, VS and VA are the amplitudes of the symmetric and antisymmetric components, respectively, of the dc mixed voltage, and ∆H is the half linewidth. qeff SH is given by (5, 9)
qSH ¼
1 eJS VS em0 MS td 4pMeff =2 1þ ¼ JC VA Hres ℏ
ð3Þ
where Meff is the effective magnetization that can be extracted by fitting the resonance frequency fres as a function of Hres using the Kittel formula (18) fres ¼ Fig. 1. ST-FMR measurement of qeff SH in p-IrMn3. (A) Illustration of the ST-FMR experimental setup where Hext is the external field, M is the magnetization of the permalloy layer (yellow), and tH and tST are the torques on M due to the Oersted field created by the RF charge current and the spin current in the Ir1−x Mnx layer (green), respectively. (B) ST-FMR spectra measured on a ~60 Å IrMn3/~60 Å Py sample at a frequency varying from 9 to 12 GHz. (C) ST-FMR spectrum measured at 9 GHz. The black solid lines are the fits with Lorentzian functions. The red and green solid lines represent the symmetric and antisymmetric Lorentzian fits, respectively. (D) Frequency dependence of measured qeff SH of ~60 Å IrMn3/~60 Å Py. (E) ST-FMR spectra measured on these devices with different thicknesses of IrMn3 at 11 GHz. Inset: Thickness dependences of the symmetric and antisymmetric components of Vmix. (F) Thickness dependence of measured qeff SH for IrMn3/~60 Å Py. Error bars correspond to 1 SD in (D) and (F).
the permeability in vacuum; MS is the saturation magnetization of the Py layer, which is measured using vibrating sample magnetometry on the unpatterned film before device fabrication; t is the thickness of the ^ is the direction of the injected spin moment. We note Py layer; and s that JS represents any spin current that is generated by the passage of the charge current through the device that gives rise to an antidamping torque. As we discuss below, there may be mechanisms beyond the conventional spin Hall effect that generate spin currents in the device. The Oersted field depends on the RF current and the thickness of the Ir1−xMnx layer d and can be expressed as Hrf ¼ 12 JC d for our experiments, in which the Ir1−xMnx films are comparatively thin (10 to 150 Å). Mixing the RF charge current through the device with the consequent oscillating magnetization of the Py layer, which affects the device resistance through its magnetoresistance, generates a dc voltage Vmix(Hext). Figure 1B shows typical ST-FMR spectra, that is, Vmix(Hext) Zhang et al. Sci. Adv. 2016; 2 : e1600759
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1 g ½ðHres þ HB ÞðHres þ HB þ 4pMeff Þ =2 2p
ð4Þ
in which HB is the in-plane exchange bias field due to the interaction between Py and the IrMn3 layer. For p-Ir1−xMnx films, the measured in-plane exchange bias field is small compared to Hres. Typical results of fitting the experimental data in Fig. 1B with Eq. 2 are shown in Fig. 1C, from which the fitting parameters VS, VA, Hres, and ∆H can be obtained. Using these parameters, qeff SH is estimated to be 0.092 ± 0.003 (at 11 GHz) based on Eq. 3. qeff SH exhibits little variation as a function of the RF excitation frequency (Fig. 1D). The dependence of the ST-FMR spectra on the thickness d of the p-IrMn3 layer is shown in Fig. 1E. From fits to these data using Eq. 2, the magnitude of VS varies little as a function of d, whereas VA increases approximately linearly with d (see inset to Fig. 1E), consistent with the larger Oersted field torques, as the RF charge current flowing in the p-IrMn3 layer increases. As shown in Fig. 1F, qeff SH shows a weak dependence on d, which suggests that the spin diffusion length in IrMn3 is small ( j↓ for AF1. When reversing the spins, for example, by a time reversal operation, an opposite spin chirality is realized as AF2. The time reversal operation simultaneously reverses the spin and velocity. Thus, the deflection direction for the electron with a given spin does not change. However, the relative amplitude of these currents change, that is, j↑ < j↓, because of the inversed spin chirality. Therefore, AF1 and AF2 exhibit opposite anomalous Hall current j AH and the same spin Hall current j s. (B and C) Ab initio calculations of the anomalous Hall conductivity (AHC) (sxy) and SHC ðszxy Þ with respect to chemical potential. The charge-neutral point is set to zero. Here, the x, y, and z axes correspond to the crystallographic 12, and [111], respectively (see the Supplementary Materials). directions½110,½ 1 Because AF1 and AF2 can be transformed into each other by a mirror reflection or a time reversal operation, they exhibit opposite signs of AHC but the same sign of SHC.
the results) but may be important in orienting the AF domains by perpendicular field annealing. Our calculations show that the noncollinear AF order in the (111) plane generates a strong anisotropy of the SHC. Calculations of the SHC and AHC are shown in table S2 for the two cases where z is along [111] and [001]; the calculations correspond to our experiments. We define the SHC by skij, which is the spin current along the i direction generated by a charge current along the j direction, in which the spin polarization of the spin current is oriented along the k axis. When the z axis is oriented along the [111] crystallographic direction and the x and y axes are aligned within the (111) plane, szxy ¼ szyx ¼ 98ðℏ=eÞ (in siemens per centimeter), thereby showing that an in-(111)-plane electric current can generate a considerable spin Hall current in the same plane. In contrast, the in-(111)-plane electric current generates a tiny spin current along the [111] direction: in this y case, we find that szx ¼ sxzy ¼ 5ðℏ=eÞ (in siemens per centimeter). Zhang et al. Sci. Adv. 2016; 2 : e1600759
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We should point out that the shape of the SHC tensor depends on the coordinate system in which the directions of spin and currents are defined. If we rotate the z axis from the [111] to the [001] direction, we obtain a different calculated SHC tensor (see table S2). The two SHC tensors before and after rotation reveal the physics of the system and can be transformed into each other by the corresponding rotational matrix (see the Supplementary Materials) (32, 33). However, the new coordinate system is convenient →to interpret results from the (001) films in our experiments. Here, the E field is along the x axis ð½1 10Þ direction, and the out-of-plane spin current is along the z axis. y We obtain szx ¼ 165ðℏ=eÞ (in siemens per centimeter), which is much larger in amplitude than that for the z along the [111] case disy cussed above [szx ¼ 5ðℏ=eÞ (in siemens per centimeter)]. These calculations are consistent with our experiments that show a larger SHC for IrMn3 with (001) orientation compared to that with (111) orientation. It is difficult to rule out other extrinsic contributions to the SHC that might affect the differences between our experimental values and our theoretical intrinsic calculations: this is a subject for future studies. The detailed values of SHC and AHC are shown in table S2 for these two cases. In summary, these results show that, for currents along directions within the (111) plane, there is negligible SHC perpendicular to this plane but that there is a fairly large SHC within the plane perpendicular to the charge current. For the (001) case, however, when current is applied along the ½1 10 direction within the (001) plane, a very significant SHC is generated along the direction perpendicular to this plane. These calculations are consistent with our speculation that the triangular AF structure generates a large SHC inside the plane of the triangular lattice defined by the Mn moments. Thus, these calculations are consistent with a large spin-orbit torque for the (001) IrMn3 samples, which is generated by a novel SHC derived from the triangular AF structure, whereas no kind of this torque is generated for the (111)-oriented samples. Also, consistent with our perpendicular field annealing experiments, we predicted that annealing in external magnetic fields of the opposite sign, would switch the AF magnetic order between AF1 and AF2, but because the magnitude and sign of the SHC are not affected by the chirality of the AF structure, the SHC is not affected, as illustrated in Fig. 7A. In our experiments, we find that perpendicular field annealing in fields of +1 and −1 T has no effect on the magnitude of the measured spin-orbit torques (see Fig. 6A). In contrast, we anticipate that positive and negative magnetic field anneal treatments will change the sign of any AHC. In summary, we have observed a giant qeff SH in (001)-oriented IrMn3 and a smaller but still substantial qeff SH for (111)-oriented IrMn3 films. qeff SH is significantly enhanced by perpendicular (but not in-plane) field cooling–induced modifications of the microscopic antiferromagnetic structure for (001)-oriented but not (111)-oriented IrMn3/Py. We show from ab initio calculations that these giant spin-orbit torques and their facet dependence arise from a novel SHC that is derived from the triangular chiral AF structure of IrMn3. The discovery of a giant spin orbit torque at magnetic interfaces with antiferromagnetic metallic films that are already widely used in spintronics makes these films multifunctional and therefore of even greater interest for spintronics and spin-orbitronic applications.
MATERIALS AND METHODS Film growth and characterization All the films were grown in 3-mtorr argon in a magnetron sputtering system with a base pressure of ~1 × 10−8 torr. The films of Ir, 6 of 8
RESEARCH ARTICLE Ir87Mn13, Ir47Mn53, Ir36Mn64, IrMn3, Ir20Mn80, Ir14Mn86, Mn, and Py were grown from the sputter targets of Ir, Ir60Mn40, Ir36Mn64, Ir22Mn78, Ir18Mn82, Ir15Mn85, Ir11Mn89, Mn, and Py, respectively. The TaN layer was grown by reactive sputtering of a Ta target in an argon/ nitrogen gas mixture (ratio, 90:10). The concentrations of Ir and Mn were determined by Rutherford backscattering spectrometry. Polycrystalline Ir1–xMnx films were grown on Si substrates (covered with 25-nm-thick SiO2). Single-crystalline (001) and (111) IrMn3 films were grown on (001) MgO and (0001) Al2O3 single-crystalline substrates, respectively. The crystalline structure and orientation of IrMn3 were studied via q-2q XRD and by cross-sectional transmission electron microscopy. High-resolution transmission electron microscopy was carried out using a 200-kV JEOL 2010F field-emission microscope. The specimens were prepared using conventional cross sectioning, using mechanical dimpling followed by lowenergy ion milling while the sample was being cooled. Device fabrication and measurement Devices for the ST-FMR measurements were fabricated using standard photolithography and argon ion milling procedures. In the first step, the rectangular microstrips (100 mm long and 10 mm wide) were formed. In the second step, two large electrical contact pads were formed from Ru/Au (5 and 50 nm). Electrical contacts were made using high-frequency contact probes. High-frequency RF current (power, 14 dBm) was provided by a swept-signal generator (Agilent HP 83620B), and the dc-mixed voltage was measured using a Keithley 2002 Multimeter. Where not otherwise specified, the ST-FMR measurements were carried out on devices that were not subject to any field anneal treatment. Ab initio calculations Ab initio density functional theory (DFT) calculations were performed to calculate the band structure of cubic IrMn3 using the Vienna ab initio simulation package (34). The generalized gradient approximation was adopted to describe the exchange-correlation interactions between the electrons in the Perdew-Burke-Ernzerhof form (35). We reproduced the in-plane noncollinear antiferromagnetic configuration of Mn atoms and obtained the band structure in fig. S10, which is consistent with previous theoretical and experimental reports (12, 27, 36). Then, we projected the DFT Bloch wave functions onto the maximal localized Wannier functions using the Wannier90 package (37). On the basis of the tight-binding Wannier Hamiltonian, we calculated the AHC and SHC. The AHC calculated in this study is consistent with that in Chen et al.’s study (12). The intrinsic SHC was calculated using the Kubo formula approach (38)
skij
" # < unk→ j Jik j un′k→ >< un′ →k j ^v j j unk→ > eℏ ¼ ∑∑f→k n 2 Im ∑ V →k n ðEnk→ En′ →k Þ2 n′ ≠n
where the spin current operator ^J ki ¼ 12 f^v i ;^s k g (where^s k is the spin operator and ^v i ¼ ℏ1
^ ∂H ∂ki
; junk→ 〉 is the velocity operator) is the eigenvector of
Hamiltonian Ĥ, and i, j, k = x, y, z. The SHC is a third-order tensor. The AHC and SHC are integrated in a k-point mesh of 101 × 101 × 101 in the first Brillouin zone. Using finer meshes of up to 201 × 201 × 201, changes the results by less than 5%. Zhang et al. Sci. Adv. 2016; 2 : e1600759
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SUPPLEMENTARY MATERIALS Supplementary material for this article is available at http://advances.sciencemag.org/cgi/ content/full/2/9/e1600759/DC1 Supplementary Materials and Methods fig. S1. Thickness dependence of the effective SHA, qeff SH , for Ir1−xMnx. fig. S2. Frequency dependence of the effective SHA, qeff SH , for Ir1−xMnx. fig. S3. Frequency dependence of qeff SH for (001) IrMn3 (top), (111) IrMn3 (middle), and p-IrMn3 (bottom). fig. S4. ST-FMR signals measured on d IrMn3/60 Å Py at an RF frequency of 9 GHz. fig. S5. XRD measured on Ir1−xMnx films with a thickness of 100 Å. fig. S6. Magnetization Ms versus in-plane magnetic field obtained for Py on (001) IrMn3 (left), (111) IrMn3 (middle), and p-IrMn3 (right) measured from vibrating sample magnetometry. fig. S7. Exchange bias field for IrMn3. fig. S8. Exchange bias field measured in (001) and (111) IrMn3/60 Å Py bilayers as a function of IrMn3 thickness after the devices were annealed in-plane in a 1-T field (30 min) via magnetoresistance measurement. fig. S9. qeff SH as a function of Cu and Au insertion layers for (001)- and (111)-oriented IrMn3/Py bilayers, respectively. fig. S10. Ab initio band structure of IrMn3. table S1. Summary of SHA, SHC, and resistivity of Ir1–xMnx based ST-FMR devices in asdeposited, unannealed films. table S2. AHC and SHC tensors.
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Giant facet-dependent spin-orbit torque and spin Hall conductivity in the triangular antiferromagnet IrMn3
2016 © The Authors, some rights reserved; exclusive licensee American Association for the Advancement of Science. Distributed under a Creative Commons Attribution NonCommercial License 4.0 (CC BY-NC). 10.1126/sciadv.1600759
Weifeng Zhang,1,2* Wei Han,1,3* See-Hun Yang,1 Yan Sun,4 Yang Zhang,4 Binghai Yan,4 Stuart S. P. Parkin1,5† There has been considerable interest in spin-orbit torques for the purpose of manipulating the magnetization of ferromagnetic elements for spintronic technologies. Spin-orbit torques are derived from spin currents created from charge currents in materials with significant spin-orbit coupling that propagate into an adjacent ferromagnetic material. A key challenge is to identify materials that exhibit large spin Hall angles, that is, efficient charge-to-spin current conversion. Using spin torque ferromagnetic resonance, we report the observation of a giant spin Hall angle qeff SH of up to ~0.35 in (001)-oriented single-crystalline antiferromagnetic IrMn3 thin films, coupled to ferromagnetic permalloy layers, and a qeff SH that is about three times smaller in (111)-oriented films. For (001)-oriented samples, we show that the magnitude of qeff SH can be significantly changed by manipulating the populations of various antiferromagnetic domains through perpendicular field annealing. We identify two distinct mechanisms that contribute to qeff SH: the first mechanism, which is facet-independent, arises from conventional bulk spin-dependent scattering within the IrMn3 layer, and the second intrinsic mechanism is derived from the unconventional antiferromagnetic structure of IrMn3. Using ab initio calculations, we show that the triangular magnetic structure of IrMn3 gives rise to a substantial intrinsic spin Hall conductivity that is much larger for the (001) than for the (111) orientation, consistent with our experimental findings.
INTRODUCTION Spin-orbitronics is an emerging field of current interest in which spin-orbit coupling gives rise to several novel physical phenomena, many of which also have potential technological significance (1, 2). Of particular interest is the spin Hall effect in which conventional charge current densities (JC) are converted to pure spin current densities (ℏ2 JS) via spin-orbit coupling within the material (3, 4). The conversion efficiency is described by the spin Hall angle (SHA) qSH = eJS/JC. One of the most widely used techniques to measure SHA is by comparing the antidamping spin torque generated by a radio frequency (RF) spin current that propagates into an adjacent ferromagnetic layer with the field torque generated by an RF charge current (2, 5–9). This technique of spin torque ferromagnetic resonance (ST-FMR) yields an effective SHA, qeff SH (because, as we discuss further below, there can be other potential sources of spin current). The largest values of qeff SH in conventional metals that have been reported to date include the heavy metals b-tantalum (2), b-tungsten (7), platinum [once the interface transparency is taken into account (9)], and bismuth-doped copper (10). A prerequisite for large qSH is significant spin-orbit coupling. Of potential interest are compounds such as Ir1−xMnx, which are antiferromagnetic for various ranges of x. These compounds are widely used in spintronic devices because of the exchange bias fields that they imprint on neighboring ferromagnetic layers that lead to a unidirectional magnetic anisotropy (11). Theoretical studies predict that chemically ordered IrMn3 should exhibit a large anomalous Hall effect (AHE) due to its unusual triangular magnetic structure (12, 13), and recent experimental studies observed large AHE in the noncollinear 1
2
IBM Research–Almaden, San Jose, CA 95120, USA. Department of Materials Science Engineering, Stanford University, Stanford, CA 94305, USA. 3International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, China. 4 Max Planck Institute for Chemical Physics of Solids, Dresden D-01187, Germany. 5 Max Planck Institute for Microstructure Physics, Halle (Saale) D-06120, Germany. *These authors contributed equally to the work. †Corresponding author. Email: [email protected]
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antiferromagnets (AFs) Mn3Sn and Mn3Ge (14–16). Here, we observed a giant qeff SH in Ir1−xMnx films and a large facet dependence of qeff SH on IrMn3, which we find can be markedly enhanced by manipulating the populations of various AF domains via annealing in magnetic fields oriented perpendicular, but not parallel, to the film layers.
RESULTS Microstrip devices, 10 mm wide and 100 mm long, are fabricated using standard optical lithography and ion milling techniques from Ir1−xMnx/permalloy (Py)/TaN films. The films are deposited by magnetron sputtering (see Materials and Methods for details) on Si(001) substrates (covered with 25-nm-thick SiO2), MgO (001) substrates, and Al2O3 (0001) substrates at room temperature (RT) in a high–vacuum deposition chamber. ST-FMR measurements are carried out by passing a high-frequency RF current into the device (JC is the charge current density in Fig. 1A) in the presence of an external field Hext that is applied in the plane at 45° to the microstrip. The charge current that flows in the Ir1−xMnx layer generates two distinct torques on the Py layer, namely, a spin-orbit torque and an Oersted field torque. The ^ is given by (5, 17) time derivative of the magnetization of Py m → → ^ ^ dm dm ^ H ef f þ am ^ H rf þ ^ ¼ gm gm dt dt
g
ℏ ^ s ^m ^Þ JS ðm 2m0 MS t
ð1Þ
→
where g is the gyromagnetic ratio; H eff is composed of the external field, the exchange bias field, and the out-of-plane demagnetization → field; a is the Gilbert damping constant; H rf is the Oersted field; ℏ 2 JS is the spin current density generated in the Ir1−xMnx layer; m0 is 1 of 8
RESEARCH ARTICLE as a function of Hext, measured on ~60 Å polycrystalline IrMn3 (p-IrMn3)/60 Å Py for RF frequencies varying between 9 and 14 GHz. As the RF frequency increases, the resonance field Hres increases, as expected from the Kittel model, and the magnitude of Vmix decreases. Vmix(Hext) has two components: an antisymmetric component due to the Oersted field–generated torque and a symmetric component that arises from the spin-orbit torque. The ST-FMR curves are fitted with symmetric and antisymmetric Lorentzian functions, according to (5, 9) "
Vmix
DH 2 DHðHext Hres Þ ¼ c VS 2 þ VA 2 DH 2 þ ðHext Hres Þ2 DH þ ðHext Hres Þ
#
ð2Þ where c is a constant, VS and VA are the amplitudes of the symmetric and antisymmetric components, respectively, of the dc mixed voltage, and ∆H is the half linewidth. qeff SH is given by (5, 9)
qSH ¼
1 eJS VS em0 MS td 4pMeff =2 1þ ¼ JC VA Hres ℏ
ð3Þ
where Meff is the effective magnetization that can be extracted by fitting the resonance frequency fres as a function of Hres using the Kittel formula (18) fres ¼ Fig. 1. ST-FMR measurement of qeff SH in p-IrMn3. (A) Illustration of the ST-FMR experimental setup where Hext is the external field, M is the magnetization of the permalloy layer (yellow), and tH and tST are the torques on M due to the Oersted field created by the RF charge current and the spin current in the Ir1−x Mnx layer (green), respectively. (B) ST-FMR spectra measured on a ~60 Å IrMn3/~60 Å Py sample at a frequency varying from 9 to 12 GHz. (C) ST-FMR spectrum measured at 9 GHz. The black solid lines are the fits with Lorentzian functions. The red and green solid lines represent the symmetric and antisymmetric Lorentzian fits, respectively. (D) Frequency dependence of measured qeff SH of ~60 Å IrMn3/~60 Å Py. (E) ST-FMR spectra measured on these devices with different thicknesses of IrMn3 at 11 GHz. Inset: Thickness dependences of the symmetric and antisymmetric components of Vmix. (F) Thickness dependence of measured qeff SH for IrMn3/~60 Å Py. Error bars correspond to 1 SD in (D) and (F).
the permeability in vacuum; MS is the saturation magnetization of the Py layer, which is measured using vibrating sample magnetometry on the unpatterned film before device fabrication; t is the thickness of the ^ is the direction of the injected spin moment. We note Py layer; and s that JS represents any spin current that is generated by the passage of the charge current through the device that gives rise to an antidamping torque. As we discuss below, there may be mechanisms beyond the conventional spin Hall effect that generate spin currents in the device. The Oersted field depends on the RF current and the thickness of the Ir1−xMnx layer d and can be expressed as Hrf ¼ 12 JC d for our experiments, in which the Ir1−xMnx films are comparatively thin (10 to 150 Å). Mixing the RF charge current through the device with the consequent oscillating magnetization of the Py layer, which affects the device resistance through its magnetoresistance, generates a dc voltage Vmix(Hext). Figure 1B shows typical ST-FMR spectra, that is, Vmix(Hext) Zhang et al. Sci. Adv. 2016; 2 : e1600759
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1 g ½ðHres þ HB ÞðHres þ HB þ 4pMeff Þ =2 2p
ð4Þ
in which HB is the in-plane exchange bias field due to the interaction between Py and the IrMn3 layer. For p-Ir1−xMnx films, the measured in-plane exchange bias field is small compared to Hres. Typical results of fitting the experimental data in Fig. 1B with Eq. 2 are shown in Fig. 1C, from which the fitting parameters VS, VA, Hres, and ∆H can be obtained. Using these parameters, qeff SH is estimated to be 0.092 ± 0.003 (at 11 GHz) based on Eq. 3. qeff SH exhibits little variation as a function of the RF excitation frequency (Fig. 1D). The dependence of the ST-FMR spectra on the thickness d of the p-IrMn3 layer is shown in Fig. 1E. From fits to these data using Eq. 2, the magnitude of VS varies little as a function of d, whereas VA increases approximately linearly with d (see inset to Fig. 1E), consistent with the larger Oersted field torques, as the RF charge current flowing in the p-IrMn3 layer increases. As shown in Fig. 1F, qeff SH shows a weak dependence on d, which suggests that the spin diffusion length in IrMn3 is small ( j↓ for AF1. When reversing the spins, for example, by a time reversal operation, an opposite spin chirality is realized as AF2. The time reversal operation simultaneously reverses the spin and velocity. Thus, the deflection direction for the electron with a given spin does not change. However, the relative amplitude of these currents change, that is, j↑ < j↓, because of the inversed spin chirality. Therefore, AF1 and AF2 exhibit opposite anomalous Hall current j AH and the same spin Hall current j s. (B and C) Ab initio calculations of the anomalous Hall conductivity (AHC) (sxy) and SHC ðszxy Þ with respect to chemical potential. The charge-neutral point is set to zero. Here, the x, y, and z axes correspond to the crystallographic 12, and [111], respectively (see the Supplementary Materials). directions½110,½ 1 Because AF1 and AF2 can be transformed into each other by a mirror reflection or a time reversal operation, they exhibit opposite signs of AHC but the same sign of SHC.
the results) but may be important in orienting the AF domains by perpendicular field annealing. Our calculations show that the noncollinear AF order in the (111) plane generates a strong anisotropy of the SHC. Calculations of the SHC and AHC are shown in table S2 for the two cases where z is along [111] and [001]; the calculations correspond to our experiments. We define the SHC by skij, which is the spin current along the i direction generated by a charge current along the j direction, in which the spin polarization of the spin current is oriented along the k axis. When the z axis is oriented along the [111] crystallographic direction and the x and y axes are aligned within the (111) plane, szxy ¼ szyx ¼ 98ðℏ=eÞ (in siemens per centimeter), thereby showing that an in-(111)-plane electric current can generate a considerable spin Hall current in the same plane. In contrast, the in-(111)-plane electric current generates a tiny spin current along the [111] direction: in this y case, we find that szx ¼ sxzy ¼ 5ðℏ=eÞ (in siemens per centimeter). Zhang et al. Sci. Adv. 2016; 2 : e1600759
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We should point out that the shape of the SHC tensor depends on the coordinate system in which the directions of spin and currents are defined. If we rotate the z axis from the [111] to the [001] direction, we obtain a different calculated SHC tensor (see table S2). The two SHC tensors before and after rotation reveal the physics of the system and can be transformed into each other by the corresponding rotational matrix (see the Supplementary Materials) (32, 33). However, the new coordinate system is convenient →to interpret results from the (001) films in our experiments. Here, the E field is along the x axis ð½1 10Þ direction, and the out-of-plane spin current is along the z axis. y We obtain szx ¼ 165ðℏ=eÞ (in siemens per centimeter), which is much larger in amplitude than that for the z along the [111] case disy cussed above [szx ¼ 5ðℏ=eÞ (in siemens per centimeter)]. These calculations are consistent with our experiments that show a larger SHC for IrMn3 with (001) orientation compared to that with (111) orientation. It is difficult to rule out other extrinsic contributions to the SHC that might affect the differences between our experimental values and our theoretical intrinsic calculations: this is a subject for future studies. The detailed values of SHC and AHC are shown in table S2 for these two cases. In summary, these results show that, for currents along directions within the (111) plane, there is negligible SHC perpendicular to this plane but that there is a fairly large SHC within the plane perpendicular to the charge current. For the (001) case, however, when current is applied along the ½1 10 direction within the (001) plane, a very significant SHC is generated along the direction perpendicular to this plane. These calculations are consistent with our speculation that the triangular AF structure generates a large SHC inside the plane of the triangular lattice defined by the Mn moments. Thus, these calculations are consistent with a large spin-orbit torque for the (001) IrMn3 samples, which is generated by a novel SHC derived from the triangular AF structure, whereas no kind of this torque is generated for the (111)-oriented samples. Also, consistent with our perpendicular field annealing experiments, we predicted that annealing in external magnetic fields of the opposite sign, would switch the AF magnetic order between AF1 and AF2, but because the magnitude and sign of the SHC are not affected by the chirality of the AF structure, the SHC is not affected, as illustrated in Fig. 7A. In our experiments, we find that perpendicular field annealing in fields of +1 and −1 T has no effect on the magnitude of the measured spin-orbit torques (see Fig. 6A). In contrast, we anticipate that positive and negative magnetic field anneal treatments will change the sign of any AHC. In summary, we have observed a giant qeff SH in (001)-oriented IrMn3 and a smaller but still substantial qeff SH for (111)-oriented IrMn3 films. qeff SH is significantly enhanced by perpendicular (but not in-plane) field cooling–induced modifications of the microscopic antiferromagnetic structure for (001)-oriented but not (111)-oriented IrMn3/Py. We show from ab initio calculations that these giant spin-orbit torques and their facet dependence arise from a novel SHC that is derived from the triangular chiral AF structure of IrMn3. The discovery of a giant spin orbit torque at magnetic interfaces with antiferromagnetic metallic films that are already widely used in spintronics makes these films multifunctional and therefore of even greater interest for spintronics and spin-orbitronic applications.
MATERIALS AND METHODS Film growth and characterization All the films were grown in 3-mtorr argon in a magnetron sputtering system with a base pressure of ~1 × 10−8 torr. The films of Ir, 6 of 8
RESEARCH ARTICLE Ir87Mn13, Ir47Mn53, Ir36Mn64, IrMn3, Ir20Mn80, Ir14Mn86, Mn, and Py were grown from the sputter targets of Ir, Ir60Mn40, Ir36Mn64, Ir22Mn78, Ir18Mn82, Ir15Mn85, Ir11Mn89, Mn, and Py, respectively. The TaN layer was grown by reactive sputtering of a Ta target in an argon/ nitrogen gas mixture (ratio, 90:10). The concentrations of Ir and Mn were determined by Rutherford backscattering spectrometry. Polycrystalline Ir1–xMnx films were grown on Si substrates (covered with 25-nm-thick SiO2). Single-crystalline (001) and (111) IrMn3 films were grown on (001) MgO and (0001) Al2O3 single-crystalline substrates, respectively. The crystalline structure and orientation of IrMn3 were studied via q-2q XRD and by cross-sectional transmission electron microscopy. High-resolution transmission electron microscopy was carried out using a 200-kV JEOL 2010F field-emission microscope. The specimens were prepared using conventional cross sectioning, using mechanical dimpling followed by lowenergy ion milling while the sample was being cooled. Device fabrication and measurement Devices for the ST-FMR measurements were fabricated using standard photolithography and argon ion milling procedures. In the first step, the rectangular microstrips (100 mm long and 10 mm wide) were formed. In the second step, two large electrical contact pads were formed from Ru/Au (5 and 50 nm). Electrical contacts were made using high-frequency contact probes. High-frequency RF current (power, 14 dBm) was provided by a swept-signal generator (Agilent HP 83620B), and the dc-mixed voltage was measured using a Keithley 2002 Multimeter. Where not otherwise specified, the ST-FMR measurements were carried out on devices that were not subject to any field anneal treatment. Ab initio calculations Ab initio density functional theory (DFT) calculations were performed to calculate the band structure of cubic IrMn3 using the Vienna ab initio simulation package (34). The generalized gradient approximation was adopted to describe the exchange-correlation interactions between the electrons in the Perdew-Burke-Ernzerhof form (35). We reproduced the in-plane noncollinear antiferromagnetic configuration of Mn atoms and obtained the band structure in fig. S10, which is consistent with previous theoretical and experimental reports (12, 27, 36). Then, we projected the DFT Bloch wave functions onto the maximal localized Wannier functions using the Wannier90 package (37). On the basis of the tight-binding Wannier Hamiltonian, we calculated the AHC and SHC. The AHC calculated in this study is consistent with that in Chen et al.’s study (12). The intrinsic SHC was calculated using the Kubo formula approach (38)
skij
" # < unk→ j Jik j un′k→ >< un′ →k j ^v j j unk→ > eℏ ¼ ∑∑f→k n 2 Im ∑ V →k n ðEnk→ En′ →k Þ2 n′ ≠n
where the spin current operator ^J ki ¼ 12 f^v i ;^s k g (where^s k is the spin operator and ^v i ¼ ℏ1
^ ∂H ∂ki
; junk→ 〉 is the velocity operator) is the eigenvector of
Hamiltonian Ĥ, and i, j, k = x, y, z. The SHC is a third-order tensor. The AHC and SHC are integrated in a k-point mesh of 101 × 101 × 101 in the first Brillouin zone. Using finer meshes of up to 201 × 201 × 201, changes the results by less than 5%. Zhang et al. Sci. Adv. 2016; 2 : e1600759
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SUPPLEMENTARY MATERIALS Supplementary material for this article is available at http://advances.sciencemag.org/cgi/ content/full/2/9/e1600759/DC1 Supplementary Materials and Methods fig. S1. Thickness dependence of the effective SHA, qeff SH , for Ir1−xMnx. fig. S2. Frequency dependence of the effective SHA, qeff SH , for Ir1−xMnx. fig. S3. Frequency dependence of qeff SH for (001) IrMn3 (top), (111) IrMn3 (middle), and p-IrMn3 (bottom). fig. S4. ST-FMR signals measured on d IrMn3/60 Å Py at an RF frequency of 9 GHz. fig. S5. XRD measured on Ir1−xMnx films with a thickness of 100 Å. fig. S6. Magnetization Ms versus in-plane magnetic field obtained for Py on (001) IrMn3 (left), (111) IrMn3 (middle), and p-IrMn3 (right) measured from vibrating sample magnetometry. fig. S7. Exchange bias field for IrMn3. fig. S8. Exchange bias field measured in (001) and (111) IrMn3/60 Å Py bilayers as a function of IrMn3 thickness after the devices were annealed in-plane in a 1-T field (30 min) via magnetoresistance measurement. fig. S9. qeff SH as a function of Cu and Au insertion layers for (001)- and (111)-oriented IrMn3/Py bilayers, respectively. fig. S10. Ab initio band structure of IrMn3. table S1. Summary of SHA, SHC, and resistivity of Ir1–xMnx based ST-FMR devices in asdeposited, unannealed films. table S2. AHC and SHC tensors.
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